Given that n is a positive prime number. Determine analytically all possible n such that 2^{n} + n^{2} is a prime number.

(In reply to

needs a second attempt by elementofsurprize)

The fundamental tenets inclusive of the problem under reference

may not be satisfied for all odd numbers n.

For example, when n= 11; we obtain, 2^11 + 11^2 = 2169 which is divisible by 9.

It may also be noted that according to conditions of the problem, n is a positive prime number.